1. APS/DFD, Nov. 20091 Baseball Aerodynamics Alan M. Nathan, University of Illinois a-nathan@illinois.edu webusers.npl.uiuc.edu/~a-nathan/pob Introduction State of our previous knowledge What we are learning from newer technologies… --about baseball aerodynamics --about the game itself Summary

2. APS/DFD, Nov. 20092 Forces and Torques on a Spinning Baseball in Flight The goal: determine the coefficients of drag, lift, and moment mg FdFd FMFM

3. APS/DFD, Nov. 20093 Real vs. “Physics 101” Trajectory: Effect of Drag and Magnus Reduced distance on fly ball Reduction of pitched ball speed by ~10% Asymmetric trajectory Optimum fly ball angle~30 o

4. APS/DFD, Nov. 20094 Some Effects of Spin Backspin makes ball rise –“hop” of fastball –increased distance of fly ball –tricky popups Topspin makes ball drop – “12-6” curveball – topspin line drives nose-dive Sidespin makes ball break toward foul pole Breaking pitches due to spin –curveballs, sliders, cutters, etc. mg FdFd FMFM

5. APS/DFD, Nov. 20095 So what do we know about C D, C L, and C M ? …prior to 2 yrs ago

6. APS/DFD, Nov. 20096 What do we know about C D ? Depends on …. Reynold’s Number –Re=  Dv/  –Re~1x10 5 @ 45 mph surface “roughness” seam orientation? spin? Summary: Existing data show factor of ~2 discrepencies Character of the “drag crisis” not well determined C D above ~100 mph not well determined

7. APS/DFD, Nov. 20097 What do we know about C L ? Depends on …. spin parameter S  R  /v Seam orientation? Reynold’s number @ fixed S? best evidence in “no”, in region of 50-100 mph In region of importance for baseball (S=0.05-0.30), data are consistent at 20% level

8. APS/DFD, Nov. 20098 Conclusion: No strong dependence on Re at fixed S  0.2 Dependence of C L on Re at fixed S

9. APS/DFD, Nov. 20099 What do we know about C M ? Almost nothing experimentally! For golf…. C M =  S  0.012S   19-24 sec @ 100 mph   [M/R 2 ]/  v (8% larger for baseball) Therefore estimate   20-26 sec @ 100 mph

10. APS/DFD, Nov. 200910 New Technologies The PITCHf/x system The TrackMan Doppler radar system

11. APS/DFD, Nov. 200911 The PITCHf/x Tracking System Two video cameras track baseball in 1/60-sec intervals (usually “high home” and “high first”) Software to identify and track pitch frame-by- frame in real time  full trajectory Installed in every MLB ballpark Image, courtesy of Sportvision

12. APS/DFD, Nov. 200912 What kind of “stuff” can one learn? Pitch speed to ~0.5 mph –at release and at home plate Pitch location to ~0.5 inches –at release and at home plate “movement” to ~2.0 inches –both magnitude and direction Initial velocity direction Pitch classification –more on this later And all these data are freely available online!

13. APS/DFD, Nov. 200913 Pitched ball loses about 10% of speed between pitcher and batter Average speed is ~95% of release speed Example: Pitch Speed--PITCHf/x vs. the gun v0v0 vfvf

14. APS/DFD, Nov. 200914 Example: Pitching at High Altitude 10% loss of velocity total movement 12” 7.5% 8” PITCHf/x data contain a wealth of information about drag and lift! Toronto Denver

15. APS/DFD, Nov. 200915 20k pitches from Anaheim, 2007: Fluctuations consistent with  x  1 inch! C d vs. v 0 vs. v 0 in 2 mph bins Example: C D from Pitchf/x

16. APS/DFD, Nov. 200916 Drag Coefficient: no evidence for “drag crisis” Good approximation: C d = 0.35±0.05 in range 70-100 mph

17. APS/DFD, Nov. 200917 Example: Pitch Classification: LHP Jon Lester, 8/4/07 catcher’s view pitches fall into neat clusters: I:4-seam FB II:2-seam FB III:slider (note the reduced spin) IV:CB

18. APS/DFD, Nov. 200918 Compare with knuckleball pitcher Tim Wakefield FB CB

19. APS/DFD, Nov. 200919 Josh Kalk, THT, 5/22/08 What makes an effective slider?—C. C. Sabathia This slider is very effective since it looks like a fastball for over half the trajectory, then seems to drop at the last minute (“late break”). side view

20. APS/DFD, Nov. 200920 New Tools to Study Trajectories of Batted Balls Hitf/x –Uses Pitchf/x cameras to track initial trajectory v 0, ,  Hittracker (www.hittrackeronline.com) –Measure landing point and flight time for home runs TrackMan Doppler radar –Tracks full batted ball trajectory –Determines initial spin Possibly spin decay

21. APS/DFD, Nov. 200921 Example: The “carry” of a fly ball How much does a fly ball “carry”? Motivation: does the ball carry especially well in the new Yankee Stadium? “carry” ≡ (actual distance)/(vacuum distance) for same initial conditions

22. APS/DFD, Nov. 200922 The “carry” of a fly ball 819 home runs from April 2009

23. APS/DFD, Nov. 200923 Fly ball trajectory from TrackMan ( Safeco Field experiment) Conclusion: Simple prescription for drag and Magnus fits data beautifully. CDCD New TrackMan pitch data

24. APS/DFD, Nov. 200924 Summary We are on the verge of major breakthrough on our ability to track baseballs and determine the aerodynamic effects In the near future we should be able to address some outstanding issues: –more precise values for C d in “crisis” region for v>100 mph –spin-dependent drag? –dependence of drag & Magnus on seam orientation, surface roughness, … –time constant for spin decay?